Copy Rotation adding rotation to start position?
There needs to be a bone for every segment like this:



The bones are connected into single chain and using inherit rotation (but this is irrelevant because it is overwritten with constraints)

In edit mode the bones were aligned with Ctrl+N > Cursor with cursor being in the center of mass of the bone chain.

Then the red mesh (the reference hair strand) has a vertex group for each vertex on the bone chain containing that single vertex:



Vertex0 is at the root.

Here is setup of every single bone exept the root bone. The root has copy location from Vertex0 as a first extra constraint in the stack:



The bones will not rotate until you simulate the red mesh now. They won't follow the mesh perfectly (that's because vertex normals and how they work) but they will follow closely. To make the chain follow perfectly the bones would have to target polygons instead of vertices (it's not supported, they can target only vertices - with vertex groups).

Here is a blend with the beginning of hair rigged: